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When you think of a machine learning algorithm, the first metric that comes to mind is its accuracy. A lot of research is centered on developing algorithms that are accurate and can predict the outcome with a high degree of confidence. During the training process, an important issue to think about is the stability of the learning algorithm. This allows us to understand how a particular model is going to turn out. We need to make sure that it generalizes well to various training sets. Estimating the stability becomes crucial in these situations. So what exactly is stability? How do we estimate it? Continue reading →

Ergodicity is one of the most important concepts in statistics. More importantly, it has a lot of real world applications. In this case, it’s applicable to the staggering number of internet connected devices in the world of Internet of Things (IoT). Most of the experiments conducted by research labs, businesses, and marketing agencies often rely on statistics to compile the results. This can be about a set of customers, voters, viewers, or any other segment. Ever wondered why the results are often inaccurate? One of the main reasons is the underlying assumption about ergodicity. What exactly is it? Continue reading →

Sequences occur everywhere in our daily life. Some of the examples include sensor data, stock market quotes, speech signals, and many more. A sequence is a collection of elements where each element is indexed. Repetitions are allowed in this case, which means any element can reappear in a given sequence. If we look closely, we can see that sequences are rich in information. In theory, we can design sequences with amazing characteristics and study them. This allows us to approximate real world processes using these sequences so that we can estimate what’s going to happen in the future. Cauchy sequence is one such sequence that’s very fundamental to a lot of fields. Let’s dig deeper and see why it’s relevant, shall we? Continue reading →

Time series data has memory. It remembers what happened in the past and avenge any wrongdoings! Can you believe it? Okay the avenging part may not be true, but it definitely remembers the past. The “memory” refers to how strongly the past can influence the future in a given time series variable. If it has a strong memory, then we know that analyzing the past would be really useful to us because it can tell us what’s going to happen in the future. If you need a quick refresher, you can check out my blog post where I talked about memory in time series data. We have a high level understanding of how we can classify time series data into short memory and long memory, but how do we actually measure the memory? Continue reading →

Let’s consider a business deal where there are multiple parties negotiating the terms. In such a situation, it’s usually not possible for every single party to get everything it wants. They need to optimize their demands so that everyone comes out with something positive. Similar situations arise across many areas of engineering where we have to deal with many resources and we need to make a trade off based on cost, quality, speed, and so on. How do we model this problem and decide the optimal state of affairs? This is where the concept of Pareto Optimality comes into picture. Continue reading →

We encounter time series data very frequently in the real world. Some common examples include real time sensors, surveillance video, stock market, astrophysics, speech recognition, and so on. In order to study time series data, we try to extract various characteristics that tend to define it. One of the most important things to think about is the dependence between various points in the time series data. Is there any dependence between the values in the time series data? If so, how far apart in time do they have to be in order to affect each other? Understanding these aspects will open up new doors in terms of how we analyze the data. This is where the concept of long memory comes into picture. Let’s dig a little deeper and understand it, shall we? Continue reading →

There are many phenomena in everyday life where it’s very difficult to model the problem. There are so many variables and so many dependencies that any approximation or assumption would lead to a huge errors in outputs. This is usually a combination of uncertainty and variability. Even though we have access to all the historical information, we can’t accurately predict a future outcome because of inaccurate modeling. This becomes especially relevant when we are dealing with systems where the degrees of freedom are dependent on each other. An example would be movement of fluids or kinetic modeling of gases. How do we compute the possible outcomes? How can we assess the impact of all the free variables to make sure we predict the outcome under uncertainty? Continue reading →